The Mathematics of Quantum Theory

关于拓扑量子场论（TQFT）和拓扑场论最新发展的国际会议将于2014年5月23-26日在加州大学戴维斯分校举行：http://indico.cern.ch/conferenceDisplay.py？这次活动将有著名数学家和理论物理学家出席，并与加州大学戴维斯分校数学系庆祝阿尔伯特·施瓦茨教授在数学和物理学领域60年杰出贡献的活动相配合。事实上，tqft最早是由施瓦茨在20世纪70年代建造的。Witten对Chern- Simons tqft的解决方案为将量子场论与严格数学联系起来的快速发展奠定了基础，特别是在统一弦和m理论模型的核心拓扑弦理论领域。同时，这些思想导致了低维拓扑数学的深刻进步；枚举几何、辛几何和代数几何；结理论，甚至非交换几何。这次会议将为研究人员提供一个独特的机会来传播他们在这些领域的最新成果，也为研究生们提供了一个看到最高水平的科学家在行动的机会。为了理解这类研究的根本重要性，我们可以从对撞机实验的最新结果开始。希格斯粒子的发现（并因其预测而获得诺贝尔奖）再次证实了量子场论在最大和最小尺度上正确地描述了我们的宇宙。公众可能会惊讶地发现，像量子场论这样重要的理论仍然不能精确地用数学定义。事实上，在这个方向上的主要进展是在拓扑理论的特殊情况下，这些理论依赖于空间和时间的整体形状（但对小的局部现象不敏感）。这次会议解决了我们目前认识中的这个缺口。对一般量子场论的严格的数学理解将导致新的数学和物理结果的爆炸，可能会彻底改变我们所知道的科学。

The Mathematics of Quantum Theory, 05/01/14-12/01/15, University of California, DavisAn international conference focusing on recent developments in topological quantum field theory (TQFT) and topological field theory will be held on May 23-26, 2014 at the University of California, Davis:http://indico.cern.ch/conferenceDisplay.py?confId=276011The event will be attended by leading mathematicians and theoretical physicists and dovetails with a U.C. Davis Department of Mathematics celebration of sixty years of spectacular contributions to mathematics and physics by Professor Albert Schwarz. Indeed TQFTs were first constructed by Schwarz in the 1970s. Witten's solution of Chern--Simons TQFTs then laid the foundation for rapid progress connecting quantum field theory to rigorous mathematics, especially in the arena of the topological string theories that lie at the heart of unified String and M-Theory models. Concurrently, these ideas have led to profound advances in the mathematics of low dimensional topology; enumerative, symplectic and algebraic geometry; knot theory and even non-commutative geometry. The conference will be a unique opportunity for researchers to disseminate their latest results in these areas as well as for graduate students to see scientists of the highest calibre in action.To understand the fundamental importance of this type of research, one can begin by considering the latest results coming from collider experiments. The discovery of the Higgs particle (and Nobel Prizes for its prediction) confirms once again that quantum field theory correctly describes our universe at the very largest and smallest scales. Members of the public might be surprised to learn that such an important theory as quantum field theory can still not be exactly defined mathematically. In fact, the main progress in this direction has been in special cases of topological theories that depend on the global shape of space and time (but are insensitive to small local phenomena). This conference addresses this gaping hole in our current understanding. A rigorous mathematical understanding of general quantum field theories will lead to an explosion of new mathematical and physical results likely to revolutionize science as we know it.